An Introduction to Fourier Transforms D. S. Sivia St. John’s College Oxford, England August 12, 2015 Outline ....................................................................... 2 Taylor Series ................................................................... 3 Taylor Series (0) ................................................................ 4 Taylor Series (1) ................................................................ 5 Taylor Series (2) ................................................................ 6 Taylor Series (3) ................................................................ 7 Taylor Series (4) ................................................................ 8 Fourier Series .................................................................. 9 Fourier Series (0) .............................................................. 10 Fourier Series (1) .............................................................. 11 Fourier Series (1) .............................................................. 12 Fourier Series (2) .............................................................. 13 Fourier Series (3) .............................................................. 14 Fourier Series (4) .............................................................. 15 Taylor Versus Fourier Series ..................................................... 16 Complex Fourier Series ......................................................... 17 Fourier Transform ............................................................. 18 Some Symmetry Properties ...................................................... 19 Convolution .................................................................. 20 Convolution Theorem........................................................... 21 Auto-correlation Function ....................................................... 22 Auto-correlation Function (1) .................................................... 23 Auto-correlation Function (2) .................................................... 24 Fourier Optics................................................................. 25 Young’s Double Slits............................................................ 26 Single Wide Slit ............................................................... 27 Two Wide Slits (0) ............................................................. 28 Two Wide Slits (1) ............................................................. 29 Two Wide Slits (2) ............................................................. 30 Two Wide Slits (3) ............................................................. 31 Finite Grating (0) .............................................................. 32 Finite Grating (1) .............................................................. 33 Finite Grating (2) .............................................................. 34 1
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An Introduction to Fourier Transforms - Neutron Scattering · Taylor Versus Fourier Series Taylor: f(x)= X ∞ n=0 an(x−xo) n |x−xo|
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